Download Allowed and Forbidden d-d Transitions in Poly(3,5

Photochemistry and Photobiology, 2006, 82:
57–63
Allowed and Forbidden d-d Transitions in
Poly(3,5-dimethylpyrazolyl)methane Complexes of Nickel(II)†
Marie-Christine Nolet, Annie Michaud, Cheryl Bain, Davit Zargarian and Christian Reber*
Département de Chimie, Université de Montréal, Montréal, Canada
Received 28 June 2005; accepted 20 September 2005; published online 22 September 2005 DOI: 10.1562/2005-06-28-RA-593
(bpm*) and tris(3,5-dimethylpyrazolyl)methane (tpm*) ligands. All
structures are shown schematically in Chart 1. These ligands offer
an opportunity to vary the coordination sphere from three nitrogen
and three oxygen atoms in [(tpm*)Ni(g1-NO3)(g2-NO3)] (1) to
four nitrogen and two oxygen atoms in [(bpm*)2Ni(g2-NO3)]NO3
(2), to five nitrogen and one oxygen atom in [(tpm*)(bpm*)Ni(g1NO3)]NO3 (3) and finally to six nitrogen atoms in [(tpm*)2Ni]I2
(4). The absorption spectra are analyzed to examine to what extent
trends such as the empirical spectrochemical and nephelauxetic
series (7,8)—both now correlated and reformulated with advanced
electronic structure calculations such as density functional theory
(9)—can be used to rationalize the variations observed within
complexes 1 to 4. A theoretical model recently developed by
Neuhauser et al. (10) is applied and shown to be a useful tool to
obtain precise excited-state energies from complete absorption band
systems, an intrinsic advantage over traditional models that use
only band maxima with often significant uncertainties. This new
approach is shown to be successful for variations among closely
related compounds, as is the case for the series of complexes
1 to 4.
ABSTRACT
Absorption spectra of four nickel(II) complexes with poly
(pyrazolyl)methane ligands are presented in the NIR-VIS-UV
region and the band system corresponding to the lowestenergy spin-allowed and spin-forbidden transitions is analyzed. A quantitative theoretical model involving coupled
electronic states provides precise energies for the lowestenergy triplet and singlet excited states and allows comparisons between complexes with a variable number of nitrogen
and oxygen ligator atoms. Singlet energies between 12 840 and
13 000 cm21 are determined for heteroleptic complexes. These
energies are in an intermediate range between those for
homoleptic complexes with either nitrogen or oxygen ligator
atoms with singlet states at approximately 12 000 and 14 000
cm21, respectively. The new theoretical approach is compared
to the traditional ligand-field parameters obtained from the
maxima of the broad, spin-allowed absorption bands.
INTRODUCTION
MATERIALS AND METHODS
Poly(pyrazolyl)alkane ligands and their metal complexes are used
extensively in inorganic and bioinorganic chemistry because of
their interesting chemical reactivity and suitability as model
compounds. (1–3) Although the electronic structure of these complexes is an important factor determining these properties, only a
few investigations of their electronic spectroscopy have been
reported. (3–6)
Nickel(II) forms a wide variety of different complexes with
poly(pyrazolyl)alkane ligands. The coordination number for these
d8 complexes is six and distorted octahedral coordination geometries are observed, with the deviations from perfect octahedral
structure imposed by the poly(pyrazolyl)alkane ligands, coordinated through their nitrogen ligator atoms. The number and type of
poly(pyrazolyl)alkane ligands are easily varied.
We report and analyze the UV-VIS-NIR absorption spectra of
four nickel(II) complexes with bis(3,5-dimethylpyrazolyl)methane
The syntheses, characterization and crystal structures of complexes 1 to 3
(A. Michaud, F.-G. Fontaine, and D. Zargarian, in press, Inorg. Chim. Acta
[2006], doi:10.1016/j.ica.2005.09.046) and 4 (11) are described in the
literature. Absorption spectra of complexes 1 to 4 in acetonitrile solution
were measured with a Cary 5E spectrometer (Varian Inc., Palo Alto, CA)
with the spectral resolution set to 2 nm from 1600 nm to 900 nm and to 1
nm for wavelengths shorter than 900 nm. Raman spectra of solid samples
were measured with a Raman microscope (Renishaw System 3000, Wottonunder-Edge, Gloucestershire, UK) using the 488.0 and 514.5 nm Argon ion
laser lines as excitation sources. The resolution of the Raman spectra is 1
cm1. The instrumental resolution of both spectrometers is higher by an
order of magnitude than the narrowest features observed in the spectra.
SPECTROSCOPIC RESULTS
Solution absorption spectra of the nickel(II) complexes 1 to 4 illustrated in Chart 1 are shown in Fig. 1. The low molar absorptivities
of 5 to 15 M1cm1 measured for the broad bands in these
spectra are typical for the three spin-allowed d-d transitions in sixcoordinate, exactly or approximately octahedral complexes of
nickel(II), as documented in a detailed compilation. (12) The band
maxima for complexes 1 to 4 are summarized in Table 1 and compared to those for selected reference compounds. The bands are
easily assigned from the Tanabe-Sugano diagram for octahedral
complexes with the d8 electron configuration, shown in Fig. 2. The
ground state is 3A2g and three spin-allowed transitions to the 3T2g,
* To whom correspondence should be addressed: Département de chimie,
Université de Montréal, C.P. 6128, Succ. Centre-ville, Montréal QC
H3C 3J7, Canada. Fax: þ1 514 343 7586; e-mail: Christian.Reber@
UMontreal.ca
This paper is part of a special issue dedicated to Professor J. C. (Tito)
Scaiano on the occasion of his 60th birthday.
Abbreviations: bpm*, bis(3,5-dimethylpyrazolyl)methane; tpm*, tris(3,5dimethylpyrazolyl)methane.
2006 American Society for Photobiology 0031-8655/06
57
58 Marie-Christine Nolet et al.
Chart 1. Schematic structures of complexes 1 to 4.
3
T1g(3F) and 3T1g(3P) excited states are observed. Broad bands are
expected for all these transitions, because the excited states arise
from electron configurations different from the ground state configuration. Symmetry labels for an idealized octahedral structure
are used throughout this analysis. Point-group symmetries of the
nickel(II) sites determined by single-crystal X-ray diffraction are
C1 for complexes 1 and 2 (A. Michaud, F.-G. Fontaine, and
D. Zargarian, accepted for publication), Cs for complex 3 (A.
Michaud, F.-G. Fontaine, and D. Zargarian, accepted for publication) and C2h for complex 4 (11). Deviations from octahedral
symmetry caused by of the mixed ligand spheres for complexes 1
to 3 do not lead to multiple band maxima for any of the spinallowed bands in Fig. 1. A formal reason for this is the high
holohedrized symmetry of the ligand-field potential (8) in these
complexes. The holohedrized symmetry, obtained for orthoaxial
complexes by replacing individual ligands along one axis by their
average ligand-field strength, is Oh for complex 1 and D4h for
complexes 2 and 3, with very similar total ligand field strengths
along the three axes, indicating that any splitting of the 3T2g and
3
T1g states for octahedral symmetry should be small. All
holohedrized symmetries contain a center of inversion, rationalizing the low molar absorptivities as a consequence of the parity
selection rule. Complex 4 also has Oh holohedrized symmetry, but
shows a particularly broad 3T1g(3F) absorption band with a width at
half height of 3340 cm1, significantly larger than the corresponding bands in [Ni(ethylenediamine)3]2þ and [Ni(o-phenanthroline)3]2þ, complexes with strong trigonal distortions where
widths of 1880 and 2030 cm1 are observed. (13,14) Both this
large width and the significantly narrower 3T2g band have been
rationalized with angular overlap calculations based on singlecrystal spectra measured at low temperature (5), which show
multiple resolved maxima for this band, as a consequence of
the strongly anisotropic nickel(II)-pyrazolyl p bonding in
[Ni(tris(pyrazolyl)methane)2]2þ, a complex closely related to 4.
A single band corresponding to a spin-forbidden transition is
observed at approximately 13 000 cm1 on the high-energy side of
the lowest-energy spin-allowed band for all complexes. Transitions
to other singlet states are too weak to be observed in the spectra in
Fig. 1. Inspection of the Tanabe-Sugano diagram in Fig. 2 indicates
Figure 1. Absorption spectra in acetonitrile solution of [(tpm*)Ni(NO3)2]
(1), [(bpm*) 2 Ni(NO 3 )]þ (2), [(tpm*)(bpm*)Ni(NO 3 )]þ (3), and
[(tpm*)2Ni]2þ (4).
that the final state of this transition is 1Eg, the lowest-energy singlet
state. It arises from the same electron configuration as the ground
state and therefore a narrow band is expected.
The band maxima of the spin-allowed transitions are traditionally used to calculate the ligand field parameters 10Dq and B with
the following equations: (13,15)
10Dq ¼ Eð3A2g ! 3T2g Þ
ð1Þ
15B ¼ Eð3A2g ! 3T1g ð3FÞÞ þ Eð3A2g ! 3T1g ð3PÞÞ 30Dq ð2Þ
All calculated values for 10Dq and B are summarized in Table 1.
The 10Dq/B ratios of 11–15 for 1 to 4 are higher than for homoleptic complexes with oxygen ligator atoms, illustrated by
[Ni(H2O)6]2þ at a 10Dq/B ratio of 9.2 (16) in Fig. 2, and lower than
the ratio of 18 for complexes with strong-field ligands such as
[Ni(o-phenanthroline)3]2þ (13–15), also included on the abscissa of
Fig. 2. It has been pointed out for several complexes (4,5,17) that
tris(pyrazolyl) ligands appear to be somewhat lower in the spectrochemical series than ligands such as bipyridine or phenanthroline,
but higher than monodentate pyrazole ligands. (18) The maxima of
the lowest-energy spin-allowed band for nickel(II) complexes
with tris(pyrazolyl)borate ligands (19) have been reported recently.
(20) A value of 11 400 cm1 was obtained for [bis(tris(3,5dimethylpyrazolyl)borate)nickel(II)], lower by only 270 cm1 than
for complex 4. In contrast, the homologue [bis(tris(pyrazolyl)borate)nickel(II)] with unsubstituted pyrazolyl groups has a band
maximum at 11 900 cm1, higher by 230 cm1 than complex 4.
This comparison shows that the energies of spin-allowed
Photochemistry and Photobiology, 2006, 82
59
Table 1. Spin-allowed band maxima measured at room temperature in solution and crystal-field parameter values for 10Dq and B calculated from
Eqs. 1 and 2 for complexes 1 to 4. All values are in cm1 except the 10Dq/B ratios, which are dimensionless
Complex
3
A2gfi3T2g
[(tpm*)Ni(NO3)2] (1)
[(bpm*)2Ni(NO3)]þ (2)
[(bpm*)(tpm*)Ni(NO3)]þ (3)
[(tpm*)2Ni]2þ (4)
[Ni(pyrazole)6]2þà
[Ni(NH3)]62þ§
[Ni(o-phenanthroline)3]2þjj
[Ni(H2O)6]2þ§
10 300
10 170
10 420
11 670
10 650
10 730
12 690
8580
3
A2gfi3T1g(3F)
16 410
16 800
17 264
18 470
17 100
17 530
19 050
14 300
3
A2gfi3T1g(3P)
10Dq
B 10Dq/B
27 040
26 750
27 366
28 330
27 500
28 110
n/a
25 370
10 300
10 170
10 420
11 670
10 650
10 730
12 690
8580
837
869
891
786
843
830
710
929
12.3
11.7
11.7
14.8
12.6
12.9
17.9
9.2
B is 1082 cm1 for the free Ni(II) ion.
à (18).
§ (16).
jj (14).
transitions for poly(pyrazolyl)methane and poly(pyrazolyl)borate
ligands are very similar and vary by amounts on the same order of
magnitude as those for different alkyl substituents on the pyrazolyl
groups. The 10Dq/B ratios for complexes 1 to 3 are between 11.7
and 12.3, very similar to the ratio of 12.2 reported for [(bis(3,5dimethylpyrazol-1-ylomethyl)aminoethane)Ni(g1-NO3)(g2-NO3)],
(17) as expected from the combination of nitrogen and oxygen
ligator atoms, and also to [Ni(NH3)6]2þ and [Ni(pyrazole)6]2þ, for
which ratios of 12.9 and 12.2 have been determined. (13,16,18)
These variations indicate that the 10Dq/B ratio is not a very
sensitive quantity for classifying complexes 1 to 4, because similar
values are obtained for chemically very different ligands.
The Raman spectra of complexes 1 to 4 show multiple distinct
peaks in the region of the metal-ligand stretching modes. All vibrational energies between 200 and 600 cm1 are listed in Table 2,
but unambiguous assignments to either metal-ligand stretching
modes or low-frequency ligand-centered vibrational modes can not
be made. In contrast, the Raman-active m3(E) vibrational mode of
the nitrate anion can be used to confirm the coordination of the
NO
3 ligands in complexes 1 to 3. Complex 4 does not contain
nitrate and can be used to assign Raman peaks to modes of the
poly(pyrazolyl)methane ligands. The m3(E) frequency of NO
3 is
1390 cm1 in the uncoordinated anion (21), and a peak is observed
at 1395 cm1 in complexes 2 and 3, assigned to the NO
3 counterions. The degeneracy of this mode is lifted for coordinated
nitrate ligands and two bands are observed. In compounds 1 to 3
they are separated by approximately 150 cm1, as summarized in
Table 2. The frequencies for both monodentate and bidentate
coordination are within the characteristic ranges established from
Raman (22) and IR (23) spectroscopy, and in agreement with the
monodentate and bidentate coordination for the nitrate ligands
defined by the crystal structures and shown in Chart 1 for complexes 1 to 3.
Within the series of compounds 1 to 4, it is not obvious to establish
the expected systematic trends along the spectrochemical and
nephelauxetic series (7–9) from the values of 10Dq and B in Table
1. Compound 4 has the highest value of 10Dq, 11 670 cm1, as
expected for its six nitrogen ligator atoms. According to the
DISCUSSION
Traditional ligand-field parameters
Complexes 1 to 4 show spin-allowed band maxima higher in
energy than those for homoleptic complexes with oxygen ligator
atoms and lower in energy than those observed for complexes with
nitrogen ligator atoms. (13,14,23) The values of 10Dq/B in Table 1
illustrate this trend, in particular when compared to the homoleptic
complexes included in the Table and on the abscissa of Fig. 2.
Figure 2. Tanabe-Sugano diagram for the d8 configuration. Triplet and
singlet states are given as solid and dotted curves, respectively. The positions of complexes 1 to 4 on the 10Dq/B abscissa are denoted by solid
triangles, based on the values in Table 1. Literature values for [Ni(H2O)6]2þ
(open square) and [Ni(o-phenanthroline)3]2þ (open circle) are given for
comparison. The rectangle indicates the region of close energetic proximity
for the lowest triplet and singlet excited states examined for complexes
1 to 4.
60 Marie-Christine Nolet et al.
Table 2.
Selected Raman frequencies in cm1
Compound
[(tpm*)Ni(NO3)2] (1)
[(bpm*)2Ni(NO3)]þ (2)
[(bpm*)(tpm*)Ni(NO3)]þ (3)
[(tpm*)2Ni]2þ (4)
Ni-ligand stretching region
222,
229,
216,
225,
258,
250,
347,
242,
327,
285,
383,
342,
349,
367,
416,
383,
406, 423, 442, 577
435
480, 491
404, 423, 488
NO3, m3(E) counterion NO3, m3 monodentateà
NO3, m3 chelate§
n/a
1395
1396
n/a
1309, 1460
n/a
1275, 1459
n/a
1325, 1482
1305, 1480
n/a
n/a
1390 cm1 (21).
à 1253–1290 cm1, 1481–1531 cm1 (22).
§ 1230–1350 cm1, 1480–1650 cm1 (22).
spectrochemical series, values for 10Dq should decrease if nitrogen
ligator atoms are replaced by oxygen atoms. Compound 1, with the
largest number of oxygen ligator atoms among the four complexes
studied here, has a 10Dq value of 10 300 cm1, significantly lower
than 4. In contrast, the intermediate complexes 2 and 3, with two
and one oxygen ligator atoms, respectively, do not show
a continuous increase of 10Dq.
These irregular trends can be rationalized qualitatively by
considering nickel(II)-N(pyrazolyl) bond lengths in tpm*, bpm*
and pyrazole complexes. The longest bonds are observed for the
[Ni(pyrazole)6]2þ complex, where average values of 2.12 Å have
been reported (18). Average bond lengths for [bis(tris(pyrazolyl)
methane)Ni] are on the order of 2.07–2.08 Å and appear to be
independent of the number of methyl substituents on the pyrazolyl
groups. (5,11) Values of the ligand field parameter 10Dq for these
complexes are given in Table 1 and reflect this difference: 10Dq
increases by approximately 10% from [Ni(pyrazole)6]2þ to complex 4. The corresponding average nickel(II)–N(bpm*) bond
lengths are slightly longer, on the order of 2.07 to 2.09 Å for
complex 3 and for [bis(bis(pyrazolyl)(2-thienyl)methane)(nitratoO,O9)nickel(II)]þ, a complex similar to 3 in which two pyrazolyl
groups of each poly(pyrazolyl) ligand are coordinated to the metal
center. (6) These slightly longer bonds are a likely reason for the
lower value of 10Dq for complex 2 compared to complex 1 and put
(bpm*) at an intermediate ligand field strength between pyrazole
and (tpm*).
The values of B for compounds 1 and 4 show the decrease
expected from the nephelauxetic series for the change from a
coordination sphere formed by three oxygen and three nitrogen
ligator atoms to a homoleptic coordination sphere formed by six
nitrogen atoms. Again, compounds 2 and 3 do not follow this
tendency, showing an increase of B with increasing number of
nitrogen ligator atoms, in marked contrast to the nephelauxetic
series and casting doubt on the reliability of trends for the values
of interelectronic repulsion parameters for similar complexes
determined from the broad absorption maxima in solution spectra.
The variations for both 10Dq and B show the limitations of
traditional ligand-field procedures for the characterization of
relatively small variations in the coordination sphere, as is the
case in the series of compounds studied here.
One obvious improvement of the ligand-field model, attempted
for several poly(pyrazolyl) complexes in the literature, is to use the
exact angular positions of the ligator atoms with the angular
overlap model. (3–6) This approach leads to a large number of
additional parameters that cannot be derived from the limited
number of transitions observed in the spectra in Fig. 1, in particular
for the complexes with a mixed ligand sphere. In view of the large
number of angular-overlap parameters, the Racah parameter B was
usually held constant for different complexes analyzed with this
model, a procedure not acceptable for our goal of characterizing the
variation of both 10Dq and the electron-electron interaction
parameter B. Another omission in the determination of 10Dq and
B with Eqs. 1 and 2 is spin-orbit coupling, traditionally not
considered to have a significant influence on the absorption band
maxima. In the following, we present an alternative approach to
characterizing the ligand field strength and electron-electron
interaction based on the lowest-energy singlet and triplet excited
states, including their significant interaction through spin-orbit
coupling, which is quantitatively included in the model.
Coupled singlet and triplet excited states
A prominent feature of the absorption spectra in Fig. 1 is the
shoulder near the lowest-energy spin-allowed 3A2g fi 3T2g band,
assigned as the spin-forbidden 3A2g fi 1Eg transition. The close
proximity of these two excited states leads to strong mixing
through spin-orbit coupling, an effect that has been analyzed in
detail for a number of homoleptic complexes of nickel(II).
(13,14,16,24,25) The mixing causes an increase of the intensity
and bandwidth of the spin-forbidden transition, leading to a band
that is easy to detect in the spectra in Fig. 1, in contrast to all other
transitions to singlet excited states, which are not observed in Fig. 1.
An important consequence of the coupled excited states is the
change of band shapes, which also influences the energies of the
band maxima. In order to analyze these effects, a quantitative
model has to be used, and calculated spectra have to be fitted to
experimental data. We apply a theoretical model to calculate the
absorption spectrum of a forbidden spin-flip transition close in
energy to an allowed interconfigurational band. This model successfully reproduces the spectra of many high-symmetry homoleptic complexes of nickel(II) and chromium(III) where coupled
electronic states of different multiplicity occur. (10,14,25) In the
following, we apply it for the first time to lower-symmetry, heteroleptic complexes. Figure 3 illustrates the model and all parameters used for the analysis.
The potential energy curves for the 3A2g ground state as well as
the 1Eg and 3T2g excited states are given by the solid curves in Fig.
3, calculated from ground state vibrational frequencies x0 obtained
experimentally from the Raman spectra summarized in Table 2 and
using the harmonic approximation. Identical frequencies were used
for all electronic states in Fig. 3. We use the symbols for all
relevant quantities defined in the original publication of this model
(10). The energy minimum of the ground-state curve corresponds
to the equilibrium geometry. Because no metal-ligand bonding
changes occur in the singlet state, its minimum is placed at the
same position as the ground state along the normal coordinate in
Photochemistry and Photobiology, 2006, 82
61
Fig. 3. The minimum for the triplet excited state is offset by xA.
The Franck-Condon maximum for the triplet band is given by the
parameter D, and the energy differences between the ground and
excited state potential energy minima are eF and eA for the singlet
and triplet excited states, respectively. The two excited states are
coupled by the constant c, expected to be similar in magnitude to
the spin-orbit coupling constant for first-row transition metal ions
and leading to the adiabatic potential energy surfaces shown as
dotted lines in Fig. 3, different from the harmonic diabatic curves.
Both sets of curves are necessary to calculate the absorption band
system arising from transitions to these coupled excited states. The
Hamiltonian for the two excited states described by the coupled
potential energy surfaces is given by:
H¼
1
Mx20 x2 þ eF
p2 1 0
þ 2
c
2M 0 1
c
1
2
Mx
ðx
xA Þ2 þ eA
0
2
ð3Þ
Analytical and numerical solutions for the absorption spectrum
resulting from transitions to these two coupled excited states have
been published and discussed (10,25). The calculated spectrum
involving the coupled states is given by
1
rðxÞ ¼
2p
Z‘ D
E
w0 jeiðHxÞt jtj jw0 dt
‘
1 D
¼ Im w0 jH x i
p
1
jw0
E
ð4Þ
The absorption spectra in Fig. 1 do not allow an experimental
determination of all triplet excited levels arising from 3T2 g split by
deviations from octahedral symmetry and spin-orbit coupling. We
describe the bandshape for the allowed transition to the triplet
excited state in the absence of coupling to p
the
singlet excited state
ffiffiffiffiffiffiffiffi
by a Lorentz profile with a width of x0 k. (10) With this
simplification, which also makes it unnecessary to specify individual normal coordinates and offsets xA, an analytical equation for
the absorption spectrum is obtained:
1
b
rðxÞ ¼ Im
p
1 c2 ab
ð5Þ
where a and b are defined as:
1
x eF þ i
1
pffiffiffiffiffiffiffiffi
b¼
x D þ i x0 k
a¼
ð6Þ
Spectra calculated with equation (5) are shown in the inset to
Fig. 3. The spectra calculated with a value of zero for the coupling
constant c are shown as Lorentz profiles denoted by dotted traces
for two different values of eA. The traces therefore differ only in
the position of the band maximum along the wavenumber axis. The
corresponding spectra calculated with a nonzero coupling constant
are shown as solid traces in the inset, indicating the important
influence of the energy difference between eA and eF. For a small
difference, a characteristic band shape with two maxima separated
by a minimum, denoted as the interference dip (10,25,26), is
Figure 3. Coupled potential energy surfaces for the ground state and the
lowest-energy singlet and triplet excited states with definition of model
parameters. The inset shows calculated spectra for two different values of
eA. Dotted and solid traces denote calculated spectra corresponding to
uncoupled and coupled excited states, respectively. The difference traces at
the bottom of the inset illustrate the effect of coupled excited states on the
shape of the absorption spectrum. The absorption baseline is given as
a thin dotted line in order to emphasize minima and maxima of the difference traces.
calculated, as illustrated by the spectrum peaking at higher energy.
The difference between this spectrum and the Lorentz profile is
given as a dotted trace at zero absorbance, and it shows the
maximum–minimum–maximum characteristic typical for coupled
excited states in molecular spectra (10), in marked contrast to
atomic spectra. (27) The band shape is less obvious for the larger
separation between eA and eF, where a spectrum with a maximum
and a shoulder is observed, also given in the inset of Fig. 2. The
difference trace for this situation is given as a solid line starting at
zero absorbance, and it again clearly shows the maximum–
minimum–maximum profile, but with a weaker low-energy maximum and a broader minimum denoting the interference dip than for
the dotted difference trace. This comparison shows quantitatively
that absorption spectra involving coupled excited states retain
a characteristic band shape with an interference dip, even if no
clearcut minimum can be distinguished in the experimental
spectrum. A model using the full set of coupled potential energy
curves shown in Fig. 3 has to be applied for a precise analysis of
these spectra, as described in the following for complexes 1 to 4.
In order to analyze experimental spectra with this model, as
many parameters as possible are set to experimental quantities.
Vibrational frequencies x0 were held constant at values observed
62 Marie-Christine Nolet et al.
Figure 5. Energies of the lowest-energy singlet (squares, 1Eg in Oh
symmetry) and triplet (circles, 3T2g in Oh symmetry) excited states as
a function of the number of nitrogen ligator atoms. Solid symbols denote
energies obtained from the spectra calculated with (Eq. 5) and shown in Fig.
4. Open symbols denote values obtained from the ligand field parameters in
Table 1 with Eqs. 1 and 6.
Figure 4. Calculated absorption spectra (solid lines) compared to
experimental traces (dotted lines) in the region of the lowest-energy singlet
and triplet transitions for complexes 1 to 4.
in the Raman spectra and initial values for D and eF were estimated
from the spectra. The coupling constant c was limited to values
below 1000 cm1, corresponding to the order of magnitude of the
spin-orbit coupling constant for nickel(II). Only k, a factor contributing to the width of the spin-allowed absorption band, and ,
a phenomenological parameter defining the shape of the spectrum
in the region of the formally spin-forbidden band, were treated as
adjustable parameters without numerical constraints. The most
important parameter values obtained from the fits are band maxima
D for the allowed transition and energies eF for the lowest-energy
singlet excited state of complexes 1 to 4.
Figure 4 shows a comparison of experimental and calculated
spectra. The agreement is excellent, and the numerical values of all
parameters used for the calculations are summarized in Table 3.
We carried out calculations with several different experimental
vibrational frequencies, because multiple totally-symmetric metalligand stretching modes are expected for complexes with a mixed
ligand sphere, such as complexes 1 to 3, or for complexes with
lower than Oh point group symmetry, such as complex 4. Numerical results for two different frequencies x0 from Table 2 are
given in Table 3 for compounds 1 and 4. The calculated spectra
Table 3. Parameter values from fits of Eq. 5 to the absorption spectra in
Fig. 4. All values are in cm1 units. Values obtained using two different
frequencies x0 are given for compounds 1 and 4
Compound
x0
k
[(tpm*)Ni(NO3)2] (1)
[(tpm*)Ni(NO3)2] (1)
[(bpm*)2Ni(NO3)]þ (2)
[(bpm*)(tpm*)Ni(NO3)]þ (3)
[(tpm*)2Ni]2þ (4)
[(tpm*)2Ni]2þ (4)
577
222
285
416
423
242
3760
9760
11728
7454
7463
14358
274
274
500
188
500
313
c
eF
D
436
397
500
228
450
243
12873
12854
12838
12994
12923
12862
10389
10370
10305
10465
11773
11765
obtained with different vibrational frequencies cannot be distinguished on the scale of Fig. 4. It is important to note that the
energies of the singlet state eF obtained from fits to the absorption
spectra using different values for the vibrational frequencies
x0 vary by less than 50 cm1, illustrating that the model is reliable
for the low-symmetry complexes with nonuniform ligand spheres
studied here. We have shown and discussed before that this approach avoids the pitfalls of 1Eg energies obtained from phenomenological procedures, such as fitting a sum of Gaussian
profiles to the observed absorption bands (14).
Comparison of model parameters
The model illustrated in Fig. 3 and leading to the calculated spectra
in Fig. 4 provides numerical values for the lowest-energy spinallowed and spin-forbidden transitions, summarized in Table 3 as
Dand eF, respectively. They are illustrated for compounds 1 to 4 in
Fig. 5 and compared to corresponding values from the traditional
ligand-field analysis, where the maximum of the lowest-energy
spin-allowed band corresponds to 10Dq, as obtained by Eq. 1 and
summarized in Table 1. The comparison of 10Dq with D shows
very similar values and an almost identical variation with the
number of nitrogen ligator atoms. The 10Dq values are systematically lower by approximately 100 cm1 than those obtained
for D, a consequence of the omission of spin-orbit coupling in the
determination of 10Dq. The magnitude of this difference is on
the order expected for spin-orbit coupling effects for complexes of
the first-row transition metal ions. Coupling between the singlet
and triplet excited states leads to the lower-energy adiabatic
potential energy curve, shown as a dotted line in Fig. 3 below the
corresponding diabatic curve denoted by a solid line. This diabatic
curve defines D, and the higher values summarized in Table 3
clearly are a consequence of coupling between the two excited
states. The comparison of the maxima for the lowest-energy spinforbidden transition to the 1Eg state is less obvious. The values for
B and 10Dq from Table 1 can be used to calculate the energy of the
Photochemistry and Photobiology, 2006, 82
1
Eg excited state. Assuming a constant ratio of the Racah
parameters C/B 5 4, its energy is given by (13):
Eð1 Eg Þ ¼ 16B 6B2 =10Dq
ð7Þ
Energies of the 1Eg state calculated with Eq. 7 are compared to
the eF values from Table 3 as the top two traces in Fig. 5. The
values for B in Table 1 lead to a large variation of 700 cm1 for the
energy of the 1Eg excited state, in contrast to the energies eF
obtained from the calculated spectra in Fig. 4, where a variation of
less than 160 cm1 as a function of the number of nitrogen ligator
atoms is observed. The parameters from the calculations in Table 3
can be used to obtain alternative values of the ratio 10Dq/B. The
model parameter D corresponds to 10Dq, and Eq. 7 can be used
with eF denoting the energy of the 1Eg state to calculate an
alternative B value. The ratio D/B obtained in this manner is 12.5
for complexes 1 to 3 and 14.2 for complex 4. This set of ratios is
closer to the expectations from the spectrochemical and nephelauxetic series than the traditional approach based on the maxima
of the spin-allowed transitions and reflects the constant 1Eg
energies observed in the absorption spectra of all complexes
studied here.
CONCLUSION
The analysis of readily obtained spectroscopic data such as the
solution absorption and solid-state Raman spectra presented here
reveals detailed information on fundamental aspects of the electronic structure of complexes with poly(pyrazolyl)methane ligands,
an important ligand system forming a variety of low-symmetry
transition metal compounds. This new approach leads to a straightforward characterization of the electronic structure and is easily
applied to other classes of complexes. Of particular interest could
be spectra with several spin-forbidden transitions, providing an
opportunity to explore trends obtained from multiple band systems
in order to gain more detailed insight into this classic problem in
the absorption spectroscopy of transition metal compounds.
Acknowledgements—This work was made possible through research
grants from the Natural Sciences and Engineering Research Council (Canada). The authors gratefully acknowledge technical help from N. Baho.
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